When a ray of monochromatic light is incident normally on glass surface, then, refracted ray

A point source $\mathrm{S}$ is placed at the bottom of different layers as shown in the figure. The refractive index of bottommost layer is ${\mathrm{\mu }}_0$. The refractive index of any other upper layer is $\mathrm{\mu }\left(\mathrm{n}\right)={\mathrm{\mu }}_0+\frac{{\mathrm{\mu }}_0}{4\mathrm{n}-18}$ A ray of light with angle $\mathrm{i}=30°$ start from the source $\mathrm{S}$. Total internal reflection takes place at the upper surface of layer having $\mathrm{n}$ equal to

How much water should be filled in a container $21 \mathrm{cm}$ in height, so that it appears half filled when viewed from the top of the container?

[given that, ${}_a\mu _w=\frac{4}{3}$]

Two thin slabs of refractive indices ${\mathrm{\mu }}_1$ and ${\mathrm{\mu }}_2$ are placed parallel to each other in the $\mathrm{x}-\mathrm{y}$ plane. If the direction of propagation of a ray the two media are along the unit vectors ${\hat{\mathrm{r}}}_1=\mathrm{a}\hat{\mathrm{i}}+\mathrm{b}\hat{\mathrm{j}}$ and ${\hat{\mathrm{r}}}_2=\mathrm{c}\hat{\mathrm{i}}+\mathrm{d}\hat{\mathrm{j}}$ then we have 

For a small air bubble, located $4 \mathrm{cm}$ below inside a glass sphere (Refractive index$\mu =1.5$) of radius $10 \mathrm{cm}$ is viewed normally from outside as shown in the figure below. Find the apparent depth (aproximately) of the bubble.

In a thin spherical fish bowl of radius $10 \mathrm{cm}$ filled with water of refractive index  $\raisebox{1ex}{$4$}\!\left/ \!\raisebox{-1ex}{$3$}\right.$, there is a small fish at a distance of $4 \mathrm{cm}$ from the centre $C$ as shown in the figure. Where will the image of fish appear, if seen from $E$ ?